In this lab students will determine the resistance of different resistors by
 | reading the code printed onto some of the resistors, |
| measuring the resistance using a Wheatstone bridge (simulation), |
| calculating the resistance using given properties of the material the resistor is made of. |
Any device that offers resistance to current flow has an equivalent resistance. If a voltmeter is used to determine the voltage V across the device and at the same time an ammeter is used to measure the current I flowing through the device, then this resistance can be found by dividing V by I, i.e. R=V/I.
The resistance of the device can also be determined with an ohmmeter. A simple ohmmeter is a voltage source V in series with an ammeter. The component, whose resistance is to be measured, is disconnected from any circuit and the ohmmeter is connected across it. The equivalent resistance is R=V/I, where I is the current flowing through the ammeter. The resistance of the component is R minus the (usually very small) resistance of the ohmmeter itself.
The accuracy of an ohmmeter is limited by its internal resistance. When extremely accurate measurements are needed, a Wheatstone bridge is used.
A diagram of a Wheatstone bridge is shown above. A Wheatstone bridge uses four resistances. R2 is precisely known, it is the reference or standard resistance. The ratio R3/R4 can be adjusted, but its value is always known. The diagram shows a single coil that is divided by the tap B. The ratio of the resistances R3 and R4 equals the ratio of the corresponding lengths of coil. This device is called a potentiometer. Rx is the resistance to be determined. A power supply with a switch is connected across points C and D, and a digital voltmeter is connected across points A and B.
The Wheatstone bridge uses a null measurement to determine the unknown resistance. When the voltmeter reads zero, the potential at A equals the potential at B. The bridge is balanced. When the bridge is balanced, the voltmeter reading does not change when the switch is opened and closed. Such null measurements are the basis for the most accurate instruments, because, when no current is flowing through the meter, the internal resistance of the meter does not affect the circuit.
If points A and B are at the same potential, then we have
I1Rx=I3R3,
I2R2=I4R4.
Since no current is flowing through the voltmeter we have
I1=I2,
I3=I4.
Therefore we have
Rx/R2=R3/R4
Rx=R2(R3/R4).
The unknown resistance is determined by reading the number n1 on the dial of the potentiometer. For the potentiometer used in this experiment, n1/10 is equal to the ratio R3/(R3+R4). We can solve for R3/R4.
R3/R4=n1/(10-n1).
We therefore have for the unknown resistance
Rx=R2(n1/(10-n1)).
Link:
| Wheatstone Bridge |
When a manual refers to a resistor, it usually refers to a device whose only purpose it is to offer resistance to current flow. The resistance of a resistor is often printed onto the resistor in code. A pattern of colored rings is used. Most resistors have three rings to encode the value of the resistance, and one ring to encode the tolerance (uncertainty) in percent. The colors of the rings are internationally defined to represent integers between 0 and 9. The integers represented by the different colors are shown in the table below.
Black |
Brown |
Red |
Orange |
Yellow |
Green |
Blue |
Violet |
Gray |
White |
0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
| The first band is the band closest to one end of the resistor. The first band and second
band together represent a two-digit integer number.
| ||
| The number represented by the color of the third band is the number of zeroes that must
be appended to the number obtained from the first two bands to get the resistance in Ohms.
(If this number is 1, you add one zero, or multiply by 101, if the number is 2,
you add two zeroes, or multiply by 102, etc.)
| ||
| The next band, (i.e. the fourth band), is the tolerance band. The tolerance band is
typically either gold or silver. A gold tolerance band indicates that the actual value
will be within 5% of the nominal value. A silver band indicates 10% tolerance.
| ||
| If the resistor has one more band past the tolerance band it is a quality band. Read the number as the % failure rate per 1000 hours, assuming maximum rated power is being dissipated by the resistor. 1% resistors have three bands to read digits to the left of the multiplier. They have a different temperature coefficient in order to provide the 1% tolerance. |
Color |
1st & 2nd |
Multiplier |
Tolerance |
| Black | 0 | 1 | -- |
| Brown | 1 | 10 | ±1% |
| Red | 2 | 100 | ±2% |
| Orange | 3 | 1,000 | ±3% |
| Yellow | 4 | 10,000 | ±4% |
| Green | 5 | 100,000 | -- |
| Blue | 6 | 1,000,000 | -- |
| Violet | 7 | 10,000,000 | -- |
| Gray | 8 | 100,000,000 | -- |
| White | 9 | -- | -- |
| Gold | -- | 0.1 | ±5% |
| Silver | -- | 0.01 | ±10% |
| No Color | -- | -- | ±20% |
The links below point to resistor color-code calculators on the web.
Links:
| Resistor Identifier |
| Resistor Color-Code Calculator |
| Find the nominal resistance of three color-coded resistors and the nominal uncertainty
in this value. Note this in table 1
below.
Table 1
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| Assume the 3 resistors are connected in series.
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| Assume the 3 resistors are connected in parallel.
|
| Assume you have 5 coils of wire. You will measure the resistance of
each of these
coils with a Wheatstone bridge and also calculate it from the material
properties.
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| You also have a standard resistance box containing 1-10 ohm precision resistors. | ||||||||||||||||||||||||||||||||
| You construct the Wheatstone bridge circuit shown below |
| Click on the link for coil 1. In the simulation, close the contact switch and rotate the potentiometer dial while observing the reading
of the digital voltmeter. Notice that the reading can be positive or negative.
Change the
dial setting until you obtain a minimum value close to zero.
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| Using the data in the table describing the coils, calculate the resistance of each coil.
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| Compare the measured and calculated values of the resistances of each of the coils of wire and calculate the percent difference. | ||||
| Repeat the measurements and calculation for each of the other coils. |
Open Microsoft Word and prepare a report using the template shown below.
| Summarize the experiment. | ||||
| Insert table 1 from part I. | ||||
| Insert table 2 from part II.
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| Is of the following statements true or false?
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Save your Word document (your name_lab7.doc) and attach it to an e-mail message to mbreinig@utk.edu.
